Question: Solve for $x$ and $y$ using elimination. ${-4x+2y = 12}$ ${-5x-2y = -30}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-9x = -18$ $\dfrac{-9x}{{-9}} = \dfrac{-18}{{-9}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-4x+2y = 12}\thinspace$ to find $y$ ${-4}{(2)}{ + 2y = 12}$ $-8+2y = 12$ $-8{+8} + 2y = 12{+8}$ $2y = 20$ $\dfrac{2y}{{2}} = \dfrac{20}{{2}}$ ${y = 10}$ You can also plug ${x = 2}$ into $\thinspace {-5x-2y = -30}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ - 2y = -30}$ ${y = 10}$